Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C

Percentage Accurate: 99.9% → 99.9%

Time: 6.2s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]

2. Final simplification 99.9%

   \[\leadsto \left(x + \sin y\right) + z \cdot \cos y \]

Alternative 2: 68.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-41}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-66}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-292}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-300}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e-41)
   (+ x z)
   (if (<= x -4.8e-66)
     (sin y)
     (if (<= x -9.6e-292) (+ z (+ x y)) (if (<= x 8e-300) (sin y) (+ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-41) {
		tmp = x + z;
	} else if (x <= -4.8e-66) {
		tmp = sin(y);
	} else if (x <= -9.6e-292) {
		tmp = z + (x + y);
	} else if (x <= 8e-300) {
		tmp = sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.4d-41)) then
        tmp = x + z
    else if (x <= (-4.8d-66)) then
        tmp = sin(y)
    else if (x <= (-9.6d-292)) then
        tmp = z + (x + y)
    else if (x <= 8d-300) then
        tmp = sin(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-41) {
		tmp = x + z;
	} else if (x <= -4.8e-66) {
		tmp = Math.sin(y);
	} else if (x <= -9.6e-292) {
		tmp = z + (x + y);
	} else if (x <= 8e-300) {
		tmp = Math.sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e-41:
		tmp = x + z
	elif x <= -4.8e-66:
		tmp = math.sin(y)
	elif x <= -9.6e-292:
		tmp = z + (x + y)
	elif x <= 8e-300:
		tmp = math.sin(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e-41)
		tmp = Float64(x + z);
	elseif (x <= -4.8e-66)
		tmp = sin(y);
	elseif (x <= -9.6e-292)
		tmp = Float64(z + Float64(x + y));
	elseif (x <= 8e-300)
		tmp = sin(y);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e-41)
		tmp = x + z;
	elseif (x <= -4.8e-66)
		tmp = sin(y);
	elseif (x <= -9.6e-292)
		tmp = z + (x + y);
	elseif (x <= 8e-300)
		tmp = sin(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e-41], N[(x + z), $MachinePrecision], If[LessEqual[x, -4.8e-66], N[Sin[y], $MachinePrecision], If[LessEqual[x, -9.6e-292], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-300], N[Sin[y], $MachinePrecision], N[(x + z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3999999999999998e-41 or 8.0000000000000002e-300 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 91.3%

      \[\leadsto \color{blue}{x} + z \cdot \cos y \]

   3. Taylor expanded in y around 0 81.0%

      \[\leadsto x + \color{blue}{z} \]

   if -3.3999999999999998e-41 < x < -4.80000000000000052e-66 or -9.6000000000000005e-292 < x < 8.0000000000000002e-300

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around 0 94.9%

      \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]

   3. Taylor expanded in z around 0 84.7%

      \[\leadsto \color{blue}{\sin y} \]

   if -4.80000000000000052e-66 < x < -9.6000000000000005e-292

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 82.5%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{z} \]

   3. Taylor expanded in y around 0 64.0%

      \[\leadsto \color{blue}{\left(x + y\right)} + z \]
   4. Step-by-step derivation

      1. +-commutative 64.0%

         \[\leadsto \color{blue}{\left(y + x\right)} + z \]

   5. Simplified 64.0%

      \[\leadsto \color{blue}{\left(y + x\right)} + z \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-41}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-66}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-292}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-300}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 3: 84.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-16} \lor \neg \left(x \leq 5.5 \cdot 10^{-225}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.3e-16) (not (<= x 5.5e-225)))
   (+ x (* z (cos y)))
   (+ (sin y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e-16) || !(x <= 5.5e-225)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = sin(y) + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.3d-16)) .or. (.not. (x <= 5.5d-225))) then
        tmp = x + (z * cos(y))
    else
        tmp = sin(y) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e-16) || !(x <= 5.5e-225)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = Math.sin(y) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.3e-16) or not (x <= 5.5e-225):
		tmp = x + (z * math.cos(y))
	else:
		tmp = math.sin(y) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.3e-16) || !(x <= 5.5e-225))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(sin(y) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.3e-16) || ~((x <= 5.5e-225)))
		tmp = x + (z * cos(y));
	else
		tmp = sin(y) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.3e-16], N[Not[LessEqual[x, 5.5e-225]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2999999999999999e-16 or 5.5000000000000002e-225 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 92.8%

      \[\leadsto \color{blue}{x} + z \cdot \cos y \]

   if -1.2999999999999999e-16 < x < 5.5000000000000002e-225

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around 0 91.5%

      \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]

   3. Taylor expanded in y around 0 78.4%

      \[\leadsto \sin y + \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-16} \lor \neg \left(x \leq 5.5 \cdot 10^{-225}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \]

Alternative 4: 98.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+32} \lor \neg \left(z \leq 5.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5e+32) (not (<= z 5.5e-5)))
   (+ x (* z (cos y)))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e+32) || !(z <= 5.5e-5)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = (x + sin(y)) + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.5d+32)) .or. (.not. (z <= 5.5d-5))) then
        tmp = x + (z * cos(y))
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e+32) || !(z <= 5.5e-5)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5e+32) or not (z <= 5.5e-5):
		tmp = x + (z * math.cos(y))
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5e+32) || !(z <= 5.5e-5))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5e+32) || ~((z <= 5.5e-5)))
		tmp = x + (z * cos(y));
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5e+32], N[Not[LessEqual[z, 5.5e-5]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999984e32 or 5.5000000000000002e-5 < z

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 99.9%

      \[\leadsto \color{blue}{x} + z \cdot \cos y \]

   if -5.49999999999999984e32 < z < 5.5000000000000002e-5

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 99.7%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+32} \lor \neg \left(z \leq 5.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]

Alternative 5: 78.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-14}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 0.00023:\\ \;\;\;\;\sin y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e-14) (+ x z) (if (<= x 0.00023) (+ (sin y) z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e-14) {
		tmp = x + z;
	} else if (x <= 0.00023) {
		tmp = sin(y) + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-8.2d-14)) then
        tmp = x + z
    else if (x <= 0.00023d0) then
        tmp = sin(y) + z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e-14) {
		tmp = x + z;
	} else if (x <= 0.00023) {
		tmp = Math.sin(y) + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.2e-14:
		tmp = x + z
	elif x <= 0.00023:
		tmp = math.sin(y) + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e-14)
		tmp = Float64(x + z);
	elseif (x <= 0.00023)
		tmp = Float64(sin(y) + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.2e-14)
		tmp = x + z;
	elseif (x <= 0.00023)
		tmp = sin(y) + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e-14], N[(x + z), $MachinePrecision], If[LessEqual[x, 0.00023], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.2000000000000004e-14 or 2.3000000000000001e-4 < x

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 97.9%

      \[\leadsto \color{blue}{x} + z \cdot \cos y \]

   3. Taylor expanded in y around 0 93.2%

      \[\leadsto x + \color{blue}{z} \]

   if -8.2000000000000004e-14 < x < 2.3000000000000001e-4

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around 0 92.4%

      \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]

   3. Taylor expanded in y around 0 72.6%

      \[\leadsto \sin y + \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-14}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 0.00023:\\ \;\;\;\;\sin y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 6: 71.2% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+20) (+ x z) (if (<= y 8.5e-6) (+ z (+ x y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+20) {
		tmp = x + z;
	} else if (y <= 8.5e-6) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.5d+20)) then
        tmp = x + z
    else if (y <= 8.5d-6) then
        tmp = z + (x + y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+20) {
		tmp = x + z;
	} else if (y <= 8.5e-6) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+20:
		tmp = x + z
	elif y <= 8.5e-6:
		tmp = z + (x + y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+20)
		tmp = Float64(x + z);
	elseif (y <= 8.5e-6)
		tmp = Float64(z + Float64(x + y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e+20)
		tmp = x + z;
	elseif (y <= 8.5e-6)
		tmp = z + (x + y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+20], N[(x + z), $MachinePrecision], If[LessEqual[y, 8.5e-6], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e20 or 8.4999999999999999e-6 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 69.6%

      \[\leadsto \color{blue}{x} + z \cdot \cos y \]

   3. Taylor expanded in y around 0 45.1%

      \[\leadsto x + \color{blue}{z} \]

   if -6.5e20 < y < 8.4999999999999999e-6

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 99.2%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{z} \]

   3. Taylor expanded in y around 0 98.7%

      \[\leadsto \color{blue}{\left(x + y\right)} + z \]
   4. Step-by-step derivation

      1. +-commutative 98.7%

         \[\leadsto \color{blue}{\left(y + x\right)} + z \]

   5. Simplified 98.7%

      \[\leadsto \color{blue}{\left(y + x\right)} + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 7: 68.9% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-86}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-174}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.3e-86) (+ x z) (if (<= x 1.05e-174) (+ y z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.3e-86) {
		tmp = x + z;
	} else if (x <= 1.05e-174) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.3d-86)) then
        tmp = x + z
    else if (x <= 1.05d-174) then
        tmp = y + z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.3e-86) {
		tmp = x + z;
	} else if (x <= 1.05e-174) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.3e-86:
		tmp = x + z
	elif x <= 1.05e-174:
		tmp = y + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.3e-86)
		tmp = Float64(x + z);
	elseif (x <= 1.05e-174)
		tmp = Float64(y + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.3e-86)
		tmp = x + z;
	elseif (x <= 1.05e-174)
		tmp = y + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.3e-86], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.05e-174], N[(y + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999987e-86 or 1.05000000000000005e-174 < x

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 89.8%

      \[\leadsto \color{blue}{x} + z \cdot \cos y \]

   3. Taylor expanded in y around 0 80.6%

      \[\leadsto x + \color{blue}{z} \]

   if -3.29999999999999987e-86 < x < 1.05000000000000005e-174

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around 0 96.5%

      \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]

   3. Taylor expanded in y around 0 50.1%

      \[\leadsto \color{blue}{y + z} \]
   4. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto \color{blue}{z + y} \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{z + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-86}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-174}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 8: 67.4% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x z))

C

double code(double x, double y, double z) {
	return x + z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + z
end function

Java

public static double code(double x, double y, double z) {
	return x + z;
}

Python

def code(x, y, z):
	return x + z

Julia

function code(x, y, z)
	return Float64(x + z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + z;
end

Wolfram

code[x_, y_, z_] := N[(x + z), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]

2. Taylor expanded in x around inf 81.8%

   \[\leadsto \color{blue}{x} + z \cdot \cos y \]

3. Taylor expanded in y around 0 70.7%

   \[\leadsto x + \color{blue}{z} \]

4. Final simplification 70.7%

   \[\leadsto x + z \]

Alternative 9: 26.5% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

public static double code(double x, double y, double z) {
	return z;
}

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]

2. Taylor expanded in x around 0 55.0%

   \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]

3. Taylor expanded in y around 0 43.6%

   \[\leadsto \sin y + \color{blue}{z} \]

4. Taylor expanded in y around 0 26.7%

   \[\leadsto \color{blue}{z} \]

5. Final simplification 26.7%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))